[en] A semiclassical approach based on the propagation of classical trajectories on potential surfaces analytically continued in to the complex plane, together with a discretization procedure, has been developed for the problem of collisional ionization. Based on Franck-Condon considerations the formalism is reduced to that of the two-state approximation. Preionization loss and tunnelling beyond turning points have not been considered. Calculated partial ionization cross sections for the Ar-He system show good agreement with a fully quantum mechanical treatment. (Auth.)